Estimation of the position of intermediate spaces for a Banach couple

Evgenii Pustylnik

Studia Mathematica (1993)

  • Volume: 107, Issue: 2, page 137-155
  • ISSN: 0039-3223

Abstract

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The position of intermediate spaces for a Banach couple is estimated with the help of its fundamental function and co-function. We study the completeness of the collection of all such functions, and the methods of calculating and estimating them for different couples. Finally, these functions are used to compare the position of spaces obtained under the action of some interpolation functors.

How to cite

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Pustylnik, Evgenii. "Estimation of the position of intermediate spaces for a Banach couple." Studia Mathematica 107.2 (1993): 137-155. <http://eudml.org/doc/216026>.

@article{Pustylnik1993,
abstract = {The position of intermediate spaces for a Banach couple is estimated with the help of its fundamental function and co-function. We study the completeness of the collection of all such functions, and the methods of calculating and estimating them for different couples. Finally, these functions are used to compare the position of spaces obtained under the action of some interpolation functors.},
author = {Pustylnik, Evgenii},
journal = {Studia Mathematica},
keywords = {position of intermediate spaces for a Banach couple; fundamental function and co-function; completeness; interpolation functors},
language = {eng},
number = {2},
pages = {137-155},
title = {Estimation of the position of intermediate spaces for a Banach couple},
url = {http://eudml.org/doc/216026},
volume = {107},
year = {1993},
}

TY - JOUR
AU - Pustylnik, Evgenii
TI - Estimation of the position of intermediate spaces for a Banach couple
JO - Studia Mathematica
PY - 1993
VL - 107
IS - 2
SP - 137
EP - 155
AB - The position of intermediate spaces for a Banach couple is estimated with the help of its fundamental function and co-function. We study the completeness of the collection of all such functions, and the methods of calculating and estimating them for different couples. Finally, these functions are used to compare the position of spaces obtained under the action of some interpolation functors.
LA - eng
KW - position of intermediate spaces for a Banach couple; fundamental function and co-function; completeness; interpolation functors
UR - http://eudml.org/doc/216026
ER -

References

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  1. [BK1] Yu. A. Brudnyĭ and N. Ya. Kruglyak, Real interpolation functors, Dokl. Akad. Nauk SSSR 256 (1981), 14-18 (in Russian); English transl.: Soviet Math. Dokl. 23 (1981), 5-8. 
  2. [BK2] Yu. A. Brudnyĭ and N. Ya. Kruglyak, Interpolation Functors and Interpolation Spaces, North-Holland, 1991. 
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  7. [DKO] V. I. Dmitriev, S. G. Kreĭn and V. I. Ovchinnikov, Fundamentals of interpolation theory for linear operators, in: Geometry of Linear Spaces and Operator Theory, Yaroslavl', 1977, 31-74 (in Russian). 
  8. [G] J. Gustavsson, A function parameter in connection with interpolation of Banach spaces, Math. Scand. 42 (1978), 289-305. Zbl0389.46024
  9. [J] S. Janson, Minimal and maximal methods of interpolation, J. Funct. Anal. 44 (1981), 50-73. Zbl0492.46059
  10. [KPS] S. G. Kreĭn, Yu. I. Petunin and E. M. Semenov, Interpolation of Linear Operators, Nauka, Moscow, 1978 (in Russian); English transl.: Amer. Math. Soc., Providence, 1982. 
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  12. [MM] L. Maligranda and M. Mastyło, Notes on non-interpolation spaces, J. Approx. Theory 56 (1989), 333-347. Zbl0668.46039
  13. [O1] V. I. Ovchinnikov, Interpolation theorems resulting from an inequality of Grothendieck, Funktsional. Anal. i Prilozhen. 10 (1976), 45-54 (in Russian); English transl.: Functional Anal. Appl. 10 (1976), 287-294. 
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  15. [P1] E. I. Pustylnik, Minimal and maximal intermediate Banach spaces, Ukrain. Mat. Zh. 29 (1977), 129-137 (in Russian); English transl.: Ukrainian Math. J. 29 (1977), 102-107. 
  16. [P2] E. I. Pustylnik, Dual Banach couples, Sibirsk. Mat. Zh. 20 (1979), 603-609 (in Russian); English transl.: Siberian Math. J. 20 (1979), 421-425. 
  17. [P3] E. I. Pustylnik, Optimal interpolation and some interpolation properties of Orlicz spaces, Dokl. Akad. Nauk SSSR 269 (1983), 292-295 (in Russian); English transl.: Soviet Math. Dokl. 27 (1983), 333-336. 
  18. [P4] E. I. Pustylnik, On some structural properties of collections of intermediate spaces of any Banach couple, in: Theory of Operators in Function Spaces, Voronezh, 1983, 80-89 (in Russian). 
  19. [P5] E. I. Pustylnik, Families of Banach spaces with a function parameter, Izv. Vyssh. Ucheb. Zaved. Mat. 1985 (8), 79-81 (in Russian). 
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  21. [S] G. Sparr, Interpolation of weighted L p -spaces, Studia Math. 62 (1978), 229-271. Zbl0393.46029

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